On ordered series and later waiting time distributions in a sequence of Markov dependent multistate trials

被引：12

作者：

Fu, JC ^{[1
]}

Chang, YM

机构：

[1] Univ Manitoba, Dept Stat, Winnipeg, MB R3T 2N2, Canada

[2] Natl Univ Kaohsiung, Dept Appl Math, Kaohsiung 811, Taiwan

来源：

JOURNAL OF APPLIED PROBABILITY | 2003年 / 40卷 / 03期

关键词：

compound pattern; ordered series pattern; later waiting time; Markov chain imbedding; transition probability matrix; probability generating function;

D O I：

10.1239/jap/1059060892

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The sooner and later waiting time problems have been extensively studied and applied in various areas of statistics and applied probability. In this paper, we give a comprehensive study of ordered series and later waiting time distributions of a number of simple patterns with respect to nonoverlapping and overlapping counting schemes in a sequence of Markov dependent multistate trials. Exact distributions and probability generating functions are derived by using the finite Markov chain imbedding technique. Examples are given to illustrate our results.

引用

页码：623 / 642

页数：20

共 28 条

[1] On probability generating functions for waiting time distributions of compound patterns in a sequence of multistate trials
Fu, JC
Chang, YM
JOURNAL OF APPLIED PROBABILITY, 2002, 39 (01) : 70 - 80
[2] On waiting time distributions for patterns in a sequence of multistate trials
Sankaran, P. G.
Midhu, N. N.
STATISTICS & PROBABILITY LETTERS, 2010, 80 (23-24) : 1798 - 1805
[3] Joint Distributions of Numbers of Runs of Specified Lengths in a Sequence of Markov Dependent Multistate Trials
Kiyoshi Inoue
Sigeo Aki
Annals of the Institute of Statistical Mathematics, 2007, 59 : 577 - 595
[4] Sooner and Later Waiting Time Problems for Runs in Markov Dependent Bivariate Trials
Sigeo Aki
Katuomi Hirano
Annals of the Institute of Statistical Mathematics, 1999, 51 : 17 - 29
[5] Sooner and later waiting time problems for runs in Markov dependent bivariate trials
Aki, S
Hirano, K
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 1999, 51 (01) : 17 - 29
[6] A NUMERICAL ALGORITHM FOR DISTRIBUTIONS OF SOONEST WAITING TIME PROBLEMS IN MARKOV DEPENDENT TRIALS
Chaderjian, Bruce
Ebneshahrashoob, Morteza
Gao, Tangan
ADVANCES AND APPLICATIONS IN STATISTICS, 2009, 13 (01) : 95 - 109
[7] On sooner and later waiting time distributions associated with simple patterns in a sequence of bivariate trials
Inoue, Kiyoshi
Aki, Sigeo
METRIKA, 2014, 77 (07) : 895 - 920
[8] On sooner and later waiting time distributions associated with simple patterns in a sequence of bivariate trials
Kiyoshi Inoue
Sigeo Aki
Metrika, 2014, 77 : 895 - 920
[9] Waiting Time Distributions of Simple and Compound Patterns in a Sequence of r-th Order Markov Dependent Multi-state Trials
James C. Fu
W. Y. Wendy Lou
Annals of the Institute of Statistical Mathematics, 2006, 58 : 291 - 310
[10] Waiting time distributions of simple and compound patterns in a sequence of r-th order Markov dependent multi-state trials
Fu, JC
Lou, WW
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2006, 58 (02) : 291 - 310

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